Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Find each sum or product. 1. 17 + 15 2. 29 + 39 3. 8(24) 4. 7(12) 5. 3(91) 6. 6(15) 32 68 192 84 273 90

Problem of the Day Determine the secret number from the following clues: The number is a multiple of 5. It is divisible by 3. It is less than 200. Its tens digit equals the sum of its other two digits. 165

Sunshine State Standards MA.6.A.3.5 Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.

Vocabulary Commutative Property Associative Property Distributive Property

Mental math means “doing math in your head.” Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

COMMUTATIVE PROPERTY (Ordering) Words Numbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15

ASSOCIATIVE PROPERTY (Grouping) Words Numbers When you are only adding or only multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4)

Caution! The Commutative and Associative Properties do not apply to subtraction or division.

Additional Example 1A: Using Properties to Add and Multiply Whole Numbers Simplify 17 + 5 + 3 + 15. Look for sums that are multiples of 10. 17 + 5 + 3 + 15 Use the Commutative Property. 17 + 3 + 5 + 15 Use the Associative Property to make groups of compatible numbers. (17 + 3) + (5 + 15) 20 + 20 Use mental math to add. 40

Additional Example 1B: Using Properties to Add and Multiply Whole Numbers Simplify 4  13  5. Look for products that are multiples of 10. 4  13  5 13  4  5 Use the Commutative Property. Use the Associative Property to group compatible numbers. 13  (4  5) 13  20 Use mental math to multiply. 260

The expressions in each row of example 1B are equivalent because they have the same value. Helpful Hint

Check It Out: Example 1A Simplify 23 + 8 + 12 + 7. 23 + 8 + 12 + 7 = 23 + 7 + 8 + 12 = 30 + 20 = 50

Check It Out: Example 1B Simplify 49 + 17 + 51. 49 + 17 + 51 = 49 + 51 + 17 = 100 + 17 = 117

Check It Out: Example 1C Simplify 6 × 33 × 5. 6 × 33 × 5 = 6 × 5 × 33 = 30 × 33 = 990

Check It Out: Example 1D Simplify 2 × 69 × 5. 2 × 69 × 5 = 2 × 5 × 69 = 10 × 69 = 690

DISTRIBUTIVE PROPERTY Words Numbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) = 60 + 24 = 84

When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

Additional Example 2A: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6  35 “Break apart” 35 into 30 + 5. 6  35 = 6  (30 + 5) Use the Distributive Property. = (6  30) + (6  5) Use mental math to multiply. = 180 + 30 = 210 Use mental math to add.

Additional Example 2B: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9  87 “Break apart” 87 into 80 + 7. 9  87 = 9  (80 + 7) Use the Distributive Property. = (9  80) + (9  7) Use mental math to multiply. = 720 + 63 = 783 Use mental math to add.

Check It Out: Example 2A Use the Distributive Property to find each product. 6  71 6  71 = 6  (70 + 1) = 6  70 + 6  1 = 420 + 6 = 426

Check It Out: Example 2B Use the Distributive Property to find each product. 28  5 28  5 = (20 + 8)  5 = 20  5 + 8  5 = 100 + 40 = 140

Check It Out: Example 2C Use the Distributive Property to find each product. 8  44 8  44 = 8  (40 + 4) = 8  40 + 8  4 = 320 + 32 = 352

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Simplify. 1. 18 + 24 + 2 + 6 2. 10  5  3 3. 13 + 42 + 7 + 8 Use the Distributive Property to find each product. 4. 8  12 5. 6  15 6. 5  34 7. 3  71 50 150 70 96 90 170 213

Lesson Quiz for Student Response Systems 1. Evaluate 16 + 23 + 4 + 7. A. 50 B. 40 C. 30 D. 20

Lesson Quiz for Student Response Systems 2. Evaluate 3  7  10. A. 140 B. 170 C. 190 D. 210

Lesson Quiz for Student Response Systems 3. Evaluate 15 + 56 + 5 + 4. A. 86 B. 80 C. 77 D. 70

Lesson Quiz for Student Response Systems 4. Use the Distributive Property to find the product. 7  15 A. 135 B. 125 C. 115 D. 105

Lesson Quiz for Student Response Systems 5. Use the Distributive Property to find the product. 4  73 A. 292 B. 282 C. 272 D. 262